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函数的值域是函数三要素之一,掌握求函数值域的方法,对于我们进一步理解函数概念、研究函数性质、确定函数最值、绘制函数图像等都会有很大的帮助,下面举例介绍几种求函数值域的常用方法.一、利用函数的单调性有些函数的值域问题,如果注重探究其单调性,那么就会较容易的解决问题.运用这种方法,要找准函数的单调区间,并阐明该函数的单调性.例1求函数y=x2+3x-槡1的值域.分析由于y=x2和y=3x-槡1在[13,
The range of the function is one of the three elements of the function, and the method of finding the value range of the function is very helpful for us to further understand the function concept, study the function property, determine the value of the function, and draw the function image. Several commonly used methods to find the value range of functions. First, the use of monotonicity Some domain functions, if you pay attention to explore its monotonicity, it would be easier to solve the problem. Using this method, to find out the function of Monotone interval, and clarify the monotonicity of the function. Example 1 Find the value of the function y = x2 + 3x-槡 1. Analysis as y = x2 and y = 3x-槡 1 in [13,